As shown in ref. [1]}, eq. (REF ) fits remarkably well the explicit results from typical modified gravity models. GR is recovered
when \(\Xi _0=1\)  (for all \(n\) ). The study of explicit modified gravity models shows that \(\Xi _0\)  can be significantly different from 1. In particular, in the RT non-local gravity model [2]} (see [3]} for review), it can be as large as \(1.80\) 
[4]}, [3]}, corresponding to a \(80\%\)  deviation from
GR.More precisely, the RT model has a free parameter \(\Delta N\) , related to the choice of initial conditions (defined by starting the evolution during a phase of primordial inflation, \(\Delta N\)  e-folds before the end of inflation) and, for large \(\Delta N\) , the prediction for \(\Xi _0\)  of the RT model saturates to the value \(\Xi _0\simeq 1.80\)  (and \(n\simeq 1.91\) ). In contrast, if the model is started with initial conditions of order one during radiation dominance, one rather finds \(\Xi _0\simeq 0.93\) , a \(7\%\)  deviation from GR.
This is quite remarkable, since the deviations from GR and from \(\Lambda \) CDM for the background evolution and scalar perturbations are observationally bounded to be much smaller, of the order of at most a few percent. Thus, the newly opened window of tensor perturbations might bring significant surprises.
